Back to School Refresher

Did you know your student could lose anywhere from two to two and a half months worth of math knowledge over the summer months? By enrolling your student at Mathnasium now, they can move ahead in their class and continue to learn new things.

Refresh their (and your) knowledge with key terms from the Mathnasium Glossary below.

addition counting “how many altogether.” The process of forming a whole.

complement “the rest of it.” the remaining part with respect to the whole.

counting the process of determining quantity (how many, how much).
denomination the collective name of a group of similar things (apples, dogs, inches).

division counting “how many of these are there inside of that.” The process of separating a whole into equal parts.

fraction the result of breaking a whole into equal parts; one or more of those equal

group one or more of the same thing (1 apple, 9 dogs, 5 inches, 8 things).

half the first fraction. A whole divided into two equal parts; one of those parts. “Two parts the same.”

interval the distance from one number (or unit) to another. The space between two numbers.

Law of SAMEness It is only possible to add and subtract things of the same kind, things with the same name, the same denomination (an apple plus a banana is not a “banapples”).

mathematics the study of wholes and parts, and the relationship between them.

matrix literally, “mother.” That which gives form, origin, or foundation to something enclosed or embedded in it. A place of origin and growth. Related words include environment, framework, womb, structure, model; enclosed, enveloping, surrounding.

measurement the determining of quantity.

multiplication counting “in equal groups.” The process of forming a whole from equal groups.

part a component of the whole. A fragment, fraction, section, portion, region; a piece broken off.

percent literally, “for each 100,” “parts per hundred,” “how many for each hundred.”

proportion literally, “according to amount.” The relation of one part to another or to the whole; relative size. Comparison, analogy, balance, symmetry.

ratio a comparsion of two numbers by division.

subtraction counting “how far apart two numbers are” and “how much is left.” The process of removing a part(s) from a whole.

whole undivided. The one composed of the many. That which can be broken–down into parts. All of the quantity under consideration.

zero the number that counts none. That which has no parts.   

- Larry Martinek

The Importance of Telling Time in a Digital Age

Most students today grow up with tablets, cell phones, and laptops at their fingertips. These tools can aid learning, but they can also encourage laziness. With the Mathnasium Method, students are taught to use their brains, not their iPads. I’ll demonstrate this by using an example of how kids can learn to tell time.

By second grade, most students can count by 1s, 2s, 5s, and 10s, up to at least 200. We can make it easy for them to “tell time” by expanding this to include counting by 15s, 20s, and 30s, as well as counting by 10s starting at any number (7, 17, 27...).

When you stop and think about it, all points on the clock can be reached quickly by counting various combinations of 30, 20, 15, 10, 5, and 1.

When students are taught these counting skills before they deal with clocks, learning how to tell time is a very straightforward process. Without these skills, it’s quite a chore.

Here’s a way to teach students these skills:

• Counting by 10s starting at any number goes like this: start at 23: twenty–three (23), thirty–three (33), forty–three (43)... as though you are just counting by 10s, except that you say the three. So, counting by 10s starting at 37 becomes thirty–seven, forty–seven, fifty–seven...

• Counting by 15s can be done by counting by 10 and then counting by 5: 15 + 15 = (15 + 5) + 10 = 20 + 10 = 30. 30 + 15 = (30 + 10) + 5 = 40 + 5 = 45. 45 + 15 = (45 + 5) + 10 = 50 + 10 = 60.

• Counting by 20s is almost the same as counting by 2s: 0, 20 (twenty), 40 (forty), 60 (sixty), 80 (eighty)...

• Counting by 30s should be presented after the child can count by 3s. Counting by 3s is similar to counting by 2s. Counting by 2s can be explained as, “Say the number, skip the next number, say the number...” Then counting by 3s becomes: “say a number, skip the next two numbers...” Now counting by 30s becomes: 0, 30 (thirty), 60 (sixty), 90 (ninety)...

With the help of parents or teachers, telling time can be introduced to a student as early as kindergarten. The sooner students learn to count quickly using the above methods, the sooner they’ll be using terms like “quarter till” and “half past.”

- Larry Martinek

When life gives you lemons...learn Math!

With Spring underway and Summer around the corner, we're already planning ways to keep your student sharp throughout the school break.  Encourage your students to utilize skills they mastered during the Summer months.  Set up a lemonade stand with reasonable prices, provide change for larger bills and let them do the math.

Counting, The Basis of Number Sense

I have often heard students coming out of a class saying, “That stuff doesn’t make sense!” This is because many students have not developed a good general sense of the mathematical subject matter that is presented at school. Students are not provided with enough context when they learn material in school. Context provides students with a suitable environment to integrate new ideas and information in a meaningful way. Unfortunately, rather than integrated learning, fragmented learning (learning without a sense of continuity) takes place in today’s schools. To fill in the gap between fragmented and integrated learning, student’s need to establish Number Sense.

So, Number Sense… what is it? Number Sense is the ability to appreciate the size and scale of numbers in the context of the question at hand. There are three elements that fall under Number Sense: counting, wholes and parts, and proportional thinking. Today we will focus on counting.

Counting, simply put, is the ability to count from any number, to any number, by any number, forward and backward. When I ask students to explain what counting is, they will usually respond by counting from 1 (1, 2, 3…). Although this is completely correct, kids need to grasp how to count from other arbitrary numbers, for instance, 28 (28, 29, 30…). How about when counting by 2s? Starting from 2 (2, 4, 6…) is easy to get down. Can our kids do the same when starting from 3 (3, 5, 7…)? After a good deal of practice, an experienced counter will know how to count to 250 by 1s forward and backward; to 300 by 2s, 5s, and 10s; and to 3,000 by 100s.

As children are learning to become experienced counters, they should also be learning how to group the numbers they count. Parents, ask your child questions like “A group of 10 take-away a group of 3 leaves how much?”

Another important idea at this stage is interval: the distance from one number to another—the space between two numbers. From 6 to 7 is 1, and from 7 to 8 is 1, making a total distance from 6 to 8 of 2. Another important aspect of counting is its connection with the basic math operations: addition (counting how much altogether), subtraction (counting how much is left), multiplication (counting in equal groups), and division (counting how many of these are in that). The basis of Number Sense begins with counting.

Remember, children don’t hate math, they hate being confused, frustrated, and embarrassed by math. Once they understand math, the passion will follow naturally.